std::complex

 

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Technical Specifications

 

Numerics library

Common mathematical functions

Floating-point environment

Complex numbers

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Compile-time rational arithmetic (C++11)

Generic numeric operations

iota (C++11)

accumulate

inner_product

adjacent_difference

partial_sum

 

std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
exp
log
log10
Power functions
pow
sqrt
Trigonometric functions
sin cos tan	asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

 

Defined in header <complex>
template< class T > class complex;	(1)
template<> class complex<float>;	(2)
template<> class complex<double>;	(3)
template<> class complex<long double>;	(4)

The specializations std::complex<float>, std::complex<double>, and std::complex<long double> are LiteralTypes for representing and manipulating complex numbers.

The effect of instantiating the template complex for any other type is unspecified.

Member types

Member type	Definition
value_type	T

Member functions

(constructor)	constructs a complex number (public member function)
operator=	assigns the contents (public member function)
real	accesses the real part of the complex number (public member function)
imag	accesses the imaginary part of the complex number (public member function)
operator+=operator-=operator/=operator*=	compound assignment of two complex numbers or a complex and a scalar (public member function)

Non-member functions

operator+operator-	applies unary operators to complex numbers (function template)
operator+operator-operator*operator/	performs complex number arithmetics on two complex values or a complex and a scalar (function template)
operator==operator!=	compares two complex numbers or a complex and a scalar (function template)
operator<<operator>>	serializes and deserializes a complex number (function template)
real	returns the real component (function template)
imag	returns the imaginary component (function template)
abs(std::complex)	returns the magnitude of a complex number (function template)
arg	returns the phase angle (function template)
norm	returns the squared magnitude (function template)
conj	returns the complex conjugate (function template)
proj (C++11)	returns the projection onto the Riemann sphere (function template)
polar	constructs a complex number from magnitude and phase angle (function template)
Exponential functions
exp(std::complex)	complex base e exponential (function template)
log(std::complex)	complex natural logarithm with the branch cuts along the negative real axis (function template)
log10(std::complex)	complex common logarithm with the branch cuts along the negative real axis (function template)
Power functions
pow(std::complex)	complex power, one or both arguments may be a complex number (function template)
sqrt(std::complex)	complex square root in the range of the right half-plane (function template)
Trigonometric functions
sin(std::complex)	computes sine of a complex number (sin(z)) (function template)
cos(std::complex)	computes cosine of a complex number (cos(z)) (function template)
tan(std::complex)	computes tangent of a complex number (tan(z)) (function template)
asin(std::complex) (C++11)	computes arc sine of a complex number (arcsin(z)) (function template)
acos(std::complex) (C++11)	computes arc cosine of a complex number (arccos(z)) (function template)
atan(std::complex) (C++11)	computes arc tangent of a complex number (arctan(z)) (function template)
Hyperbolic functions
sinh(std::complex)	computes hyperbolic sine of a complex number (sh(z)) (function template)
cosh(std::complex)	computes hyperbolic cosine of a complex number (ch(z)) (function template)
tanh(std::complex)	computes hyperbolic tangent of a complex number (function template)
asinh(std::complex) (C++11)	computes area hyperbolic sine of a complex number (function template)
acosh(std::complex) (C++11)	computes area hyperbolic cosine of a complex number (function template)
atanh(std::complex) (C++11)	computes area hyperbolic tangent of a complex number (function template)

Non-static data members

For any object z of type complex<T>, reinterpret_cast<T(&)[2]>(z)[0] is the real part of z and reinterpret_cast<T(&)[2]>(z)[1] is the imaginary part of z. For any pointer to an element of an array of complex<T> named p and any valid array index i, reinterpret_cast<T*>(p)[2*i] is the real part of the complex number p[i], and reinterpret_cast<T*>(p)[2*i + 1] is the imaginary part of the complex number p[i] These requirements essentially limit implementation of each of the three specializations of std::complex to declaring two and only two non-static data members, of type value_type, with the same member access, which hold the real and the imaginary components, respectively.

(since C++11)

Literals

Defined in inline namespace std::literals::complex_literals
operator""ifoperator""ioperator""il (C++14)	A std::complex literal representing pure imaginary number (function)

Example

Run this code

#include <iostream>
#include <iomanip>
#include <complex>
#include <cmath>
 
int main()
{
    using namespace std::literals;
    std::cout << std::fixed << std::setprecision(1);
 
    std::complex<double> z1 = 1i * 1i;     // imaginary unit squared
    std::cout << "i * i = " << z1 << '\n';
 
    std::complex<double> z2 = std::pow(1i, 2); // imaginary unit squared
    std::cout << "pow(i, 2) = " << z2 << '\n';
 
    double PI = std::acos(-1);
    std::complex<double> z3 = std::exp(1i * PI); // Euler's formula
    std::cout << "exp(i, pi) = " << z3 << '\n';
 
    std::complex<double> z4 = 1. + 2i, z5 = 1. - 2i; // conjugates
    std::cout << "(1+2i)*(1-2i) = " << z4*z5 << '\n';
}

Output:

i * i = (-1.0,0.0)
pow(i, 2) = (-1.0,0.0)
exp(i, pi) = (-1.0,0.0)
(1+2i)*(1-2i) = (5.0,0.0)

See also

C documentation for Complex number arithmetic